Consider a two particle system with particles having masses m_1 and m_2 . If the first particle is pushed towards the centre of mass through a distanc - Physics MCQ AIEEE 2006 2026 | ExamTest.live

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Consider a two particle system with particles having masses m_{1} and m_{2} . If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

Solution & Step-by-step Explanation

For the center of mass to remain stationary, Δ X_{c m} = 0 . \frac{m _{1} Δ x _{1} + m _{2} Δ x _{2}}{m _{1} + m _{2}} = 0 ⟹ m_{1} Δ x_{1} + m_{2} Δ x_{2} = 0 Let the first particle move by d towards CM (Δ x_{1} = d).To keep CM same, the second particle must move by x towards CM (Δ x_{2} = - x). m_{1} d + m_{2} (- x) = 0 m_{2} x = m_{1} d ⟹ x = \frac{m _{1}}{m _{2}} d

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Consider a two particle system with particles having masses m_{1} and m_{2} . If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

d

\frac{m _{2}}{m _{1}} d

\frac{m _{1}}{m _{1} + m _{2}} d

\frac{m _{1}}{m _{2}} d

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